Slide rule



Nov. 12, 1940. H. c. GooDRlcH SLIDE RULE Filed Nov. 9, 1939 6- Sheets-Sheat 4 NOV. 12, 1940. H Q GQQDRlCH 2221,476

SLIDE RULE Filed Nov. 9, 1939 6 Sheets-Sheet 5 Patented Nov. 12, 1940 UNITED STATES PA'ri-:NT lOFFICE.

SLIDE RULE Howard C. Goodrich, McDonald. Ohio Application November 9, 1939, Serial No. 303,687

13 claims.

This invention relates to a slide ruie or device ior calculating the value of varlables in a series of interdependent mechanical operating units, and particularly to a muiti-slideruie or device g for determining the variable factors invoived in setting' up the individual roll stands of a mili train.

This application is a continuation-in-part of applicant's copending application, Serial No.

1. 109,961, iiled November 9, 1936.

One of the objects of this invention is to provide a multi-slide ruie or device by which the value of each variable factor in a series of inter-` dependent or correlated mechanical operating ll units can be directly determined and coordinated with sil of the other operating factors which are invoived in the series.

It is another object oi' the invention to provide a multi-slide rule or device for soiving problems which invoive more than one equation or set of relations between the variables entering into the general problem wherein some of the variables are known, and others, as many as there are equations in the case to be solved, are unknown.

za It is a further object of the present lnvention to provide a simple and inexpensive multi-slide ruie or device by which the mili operator can easily and conveniently determine the adiustment necessary on each roll stand of a mili train eo for providing a nnished sheet of a predetermined thiekneas.

It is still another object of the invention to provide a multi-slide ruie or device by which the mili operator can quickly and accurately determine the adjustment and setting necessary for each roll stand of a mili train when the desired thickness oi' the flnished metal and the reduction capacities and speed ranges of the several mili stands are known.

40 Various other objects and advantages of this invention will be more apparent in the course of the following specification and will be particuiarly pointed out in the appended claims.

In the accompanying drawings there is shown,

u ior the Purpose of Illustration, one embodiment which my invention may assume in practice.

In these drawings:

Il'iaure i is a plan view o! a continuous rolling mili system of the type with which the improved w slide rule or calculator of my invention is adapted to be used:

Figure 2 is a longitudinal section through the roll stands thereof;

Figure 3 is a plan view of the improved slide u rule or calculator of my invention;

' ll'igureisan enlarged rragmentary plan view of the lower portion of the slide ruie as shown in Figura 3, showing the scales representing the roll 090111118. Il'igure 5 is an enlarged iragmentary plan view taneously to elongation in the several re of the middle portion of the ruie showin scales representing the percentage oi recii Figure 6 is a sectional view taken m. VI-VI of Fisure 5;

Figure 7 is an enlarged iragmentary pls of the upper portion of the slide ruie showi bridge and the scales representing the roll i r a Fizul'e 10 is a similar view showing 1511 modiiicatlon. The improved slide ruie or calculator invention is shown and described as lt is mi for use in determining the adjustments nef in each of the roll stands of a mili 'tr continuous type rolllng' mili system, hut understood that this is inerely for the pni." Illustration and that a slide rule or cal' similar in design may i In a continuous type roliing generally known, the product m jected to a reduction of thickmz` of themili train, and the operation and ;w ance in any one roli stand obviously nite relation to the preceding and tube A stands.

A general discussion o! the problem. in the operation of a continuous rolliiu; tem will first be stated in order to o skilied in the art to understand the na function of the slide rule or 'calculator present invention.

A fundamental condition of operation type of mlll system is that equal Volumen o uct material must pass through each, in equal periods of time. If this conditi maintained, either of two diiiicultes 'w tably result: (i) If the volume of 1118*' ing through a given mili stand ie the volume deiivered by the precediug excess loop of material is developed ile' two stands. VThis loop is likely to inne lap, and be drawn between the mile or twisted condition. This results in w the' material, marring and often brania roils and the miil drive, resuiting' in, a expensive repairs, and loss of produotioci., any mili stand tends to pull the matei in greater. volume than can be supgv'ilirfll precedlng mili stand, tension is deveiope material between these standa. .This '31ml and will be frequently hereinafter referred to. In order to obtain the proper metailurgical characteristics in the product, and also to properly proportlon the power requirements among the individual stands of the mili, the portion of the total reduction in thickness that is desired to be accomplished in each individual stand must be considered. This is referred to as percent By the use of a formula obtained from Equaw tion 7,

IOOT* reduction. T mi 10 100,1* 100-Pn (7) P''-100 pewni-7(111)' qmgw 100-15 This value is Originally calculated, for each m 12,5 stand. by the mill designer, for the proposed T 35' range of products to be rolled on the mlll. From Tm 147 an average P and maximum P for each stand, and other pertinent'data, the designer calcu- In a' mm manner'., 196 lates the average and maximum horsepower re- T8: '280 quirements for the stand and selects the proper T.,: '431 size of motor. Once the mill is built, the value T: '718 of P remains very close to an average figure. 1,.,:12136 When this figure is known for each type of prod- T4:1'994 uct, T for each stand can be easily calculated.

The values are now tabuiated for a charactertesmaffly recm'ded m the Operistic mili train. A11 of these figures are obtained a Ths 1 e :mm the mm designer. It wm be not-.ed mat e "i e f K is next flmted' Sing 'the stands Nos. I. 2 and I are not considered. This W for No' H Stand m Equatmn 6' (m3 15 is due to the condition (a common one) that in the 0m? Stand for which the necessary figm'es this portion of the train the bar or slab is never e as yet available) in more than one set of rolls at a time; hence K TMXDHXRlx it is unnecessary to correlate these stands. In G11 other words, Equation 1 hereinbefore referred to K .125 21.340330 is true only when the bar is in two or more stands 160' g at the same time. K -547.43

'5 'rmx L-contz'num miu-8 mam m wmmuous train smd No.

Gear Minir ummotorR P M... z) g; 7 g g 2% Lg Lg Maximum motor R. P M.. w) 500 440 400 400 400 400 400 Normal percent reduction... 28 40 35 30 25 15 Maximum thickness 3. 650 2750 1.800 1.400 1.000 0. 730 0.690 0.550

sse'ssfss...

21s .as .zz-s W' W 0-0 Mxmmummudimewf] I 10.000 10.000 171000 171000 ;11% 31% It is from this table, and from various metal- 50 lurgical and production requirements, that the operator must calculate his "mill setup." It will be assumed that the customer's order calls for strip 0.125 inch thick, and, for convenience, assume that the metallursical requirements are 58 normal, allowing the operator to use the normal percent reductions for each stand. It will also be assumed that production requirements will be met by a mili delivery speed of 330 R. P. M. on the last stand. The values of D are obtained 00 from the roll shop foreman, who usually paints them on the end of each roll. The operator now constructs a chart substantially as follows:

The value of R for stand No. II is now calculated:

KGw R10 T10 D10 In a like manner by use of the above equation:

All of these values-are entered on the operator's chart, which now appears as follows:

'lhe operator then cbecks to determine ii the indicated revolutions per minute of each stand are within the available range of the respective stands. I! not, a new speed for land No. ll

'I'heseriesoiroll standsofthemilltrainhereinbetore reierredtoareshown diagrammatically inrigureshandoithedrawings. Itwillbe 4 or calculator for use with the continuous mill hereinbeiore dlscussed.

As shown in Flgure 8 of the drawings, the hnproved slide rule of my invention comprises a rectangular shaped body member ll having a' plurality of slots or guide grooves ll suitably arranged therein in side by side relation and parallel to each other and extending longitudinally thereof. These slots are preiersbly iormed by embedding a plurality oi' longltudinally extendingspacedapart'l'-shapedmembers`inthe base. At one end. preferably the lower end o! thebodymember ||,ther eissecurely arranged in any suitable manner in each ot the alternate slotsorgrooveslld,athicknessscale'l'inparallel relation to each others as is more clearly showninl'lgure3,whlchrepresentsthedistance between the rolls o! the respective stands Nos. lthrough li.

Itwillbeunderstoodthatallthescslesonthe rule have a logarithmic ruling o! any suitable baseandithasbeenioundthatabaselllogarithmic scale. measuring 10 inches to the cycle.

= lOX 1.2633

= 12.833 inches The location oi' the decimal point is not consideredontheordinaryslidemle. Onthisdevice. however. the ruiingsareindexed toindicate direct reading. No. li thiekness scale. tor example,ismarkedirom.080inchto.550inchat suitable intervals along the scale.

Asismonclearlyshowninlfisures'land, thereisslidablyarrangedineachoitheslots ilo adlaeent the top end oithe bodymember il oppositetherollspacingscales'r.amovabieslide member il having a pair oi logarithmic scales arrangedtbereonwithoneoi'thescalesDrepresentingthediameteroi'therollsandtheother scaleflthereinrepresentingthespeedoi'ths motoroitherespective stands. Thereismovably arranged above and transversely oi the slidemembers llandthebodymember ||.amovable plate-like bridge or slidable member |`I to which theupperendsoieachoitheslidemembers le are releasably attached by means or a clamping thumb screw ll. There is arranged in the bridge member ll a pluraiity ot window openings il, with one positioned oppoaite each o! the slide members I.. Iachot the windows II has akniie edge or other suitable pointer or indicating means associated therewith which is fixed to the bridge member.l 'I'he entire bridge plate asssmbly is arranged to slide longi oithebodymember ll andadaptedtobelocked thereto by means o! a pair o! clamping thumb screws Il cooperating with the body member, and the slide members ll are slidably arranged relativetoboththebodymemberandthebridge member The logarithmic scale R. indicating the maximumtotheminimumspeedsotthemotorot each roll stand is marked along the lower portion ot each o! the respective slide members ll andthescaleisinvertedwithrespecttothe thickness scales 'I' tor reasons hereinai'ter to be explained. Thisscaleisalsoindexedsothatit indicates a direct reading and the slide member corresponding to No. il stand is indexed from 200 to 400. representing revolutions per minute o! the motor o! that stand and the other scales are similarly indexed to correspond to the speeds of the respective motors of each of the roll stands.

By the use of formula No. 10, it will be found that the length of the scales representing the speed of the vmotor should be 3.010 inches for each stand of this particular mill and that the length of the scales representing the diameter of the rolls for the last six stands, namely stands Nos. i through should be 0.483 inch and for the first two stands, namely, stands Nos. l and 5, should be 0.637 inch. The scales representing the diameter of the rolls are disposed opposite each of their respective windows |9 in the bridge member and are inverted relative to the scales representing the speeds of the motor and extend from the minimum to the maximum roll sizes as shown in Table I. The knife edge of each of the windows I! cooperates with the roll diameter of the respective slides to indicate the reading' thereon. There is preferabiy a blank space between each of these two scales so that the portion of the bridge plate between each of the windows and the speed scales will not mask or cover the scale markings on the respective slide members IB.

There is slidably arranged in each of the slots or grooves IS, preferably by means of a longitudinai groove arrangement between each of the thickness scales T and the slide members IB disposed in the altemate slots IS', a longitudinally extending slide member 2| having a pointer 22 or other suitable indicating means securely arranged therewith .adjacent the bottom end thereof which cooperates with the thickness scale T. The minimum length of each of the slides 2| is the sum of the lengths of the thickness scale T and the speed scale R representing the respective roll stands.

Each of the slides 2| is adapted to be releasably clamped to the body member Il by means of a clamping thumb screw 28 arranged intermediate the length thereof. On the upper or opposite end of each of the slides 2| there is securely fixed thereto a similar pointer 2| or other suitable indicating means which cooperates with speed scale R on each of the respective slide members II. However, in constructing and assembling the rule the pointer 2| on the top end of the slide 2| representing the last roll stand or stand No. is first securely fixed to that slide. A typical "setup" for the mili train, as shown in Table III is then made, and from this chart all the slides 2| are positioned so that the lower pointers 22 indicate the correct reading on each of the respective thickness scales T. Each of the slides IG is then positioned so as to indicate through the windows |9 the correct slzes of the roils on the roll diameter scales D of the respective roll stands andeach of the siides IB is clamped to the bridgemember by means of the clamping screws |8. The bridge member together with the slide members IB rigidly clamped thereto is then moved downwardly on the body member until the pointer 24 on the upper end of the slide 2| representing roll stand No. indicates the correct speed on speed scale R of the respective slide IS, The bridge member together with the slides |8 carried thereby is then locked in position by means of the pair of clamping screws 20. Each of the other upper pointers 2| is then securely fixed to its respective slide 2| so that it indicates the correct reading on the respective speed scales R on the slide Hi of the respective roll stands as shown by the ,located in such a position as to give t will readily be observed and it will be that pointer 2| also soiidly fixed to Table No. III. Thus, it will be seen t of the slides IS and each of the respective 2| constitutes a piurality of sets of slides i; any one respective pair or set represents stand.

The percentage of reduction indicia men'ihefi" 25 are now assembied on the rule. It venient to make these members equal in to the combined width of the slide 2| and ness scale T, less suflicient clearance. U. centage of reduction scale P on the indici. bers 25 is also logarithmic, having the same and cycle as the other scales, and is' liwe 'i with respect to the thickness scales T.. ne portion of the iogarthmic scale from .4 to Ii. is chosen as being the most convenient, since it covers a range from zero percent to sixty pen' cent reduction, but any range equai to, or greater than, the percent reduction range of the parm ticular stand to which it applies will be shit These scales are lndexed with a zero per at the 1.0 ruling, a ten percent at the .9 W a twenty percent at the .8 ruling, etc. The son for this is apparent from a study of Form? '7. These are securely fixed in any suitable 1 ner to the slides 2| preferably in a straight across the rule, so that a quick glance at rule will indicate any Variation from characte. istic percent reductions on any mill "setup- The index pointers, preferably arrow-heads 2G ings indicated ori the uSetup" Table No. Ina will be understood that all of the scales bered 4 through represent the roll stands l through respectively. This completes construction and calihration of the rule rr; use will now be explained.

Attention is directed to the fundamentai 1' formula:

Gl G2 and the effect of varying the more of the factors in any of equation, or of all members 'at the the slide rule of the present invention 'per this function easily and accurately The Variation of the factor T in owrelations of the equation only will sidered. It will be obvious that a eonsta for the entire set must be maintained by spondingly increasing the value of some o factor if the value of T is decreased and vi ;i w. versa. If the slide rule is operated to increi or decrease the value of T for any one st it is done. by moving only the slide 2i, iea the bridge assembly clamped at 20 and 'the |8 clamped at IB. When the slide is rele at 23 and moved up and down so that 22 indicates varying thickness, it will be moves up and down therewith indicatin Vary speeds on scale R. Since both R and T logarithmic scales on the same base and w the same length of cycle, it will 'be seen the product of the values of R and will a constant for any particular "setup." 'I'his f maintains the Equation 6 by keeping a consta' value for the member in which the factors varied. The thickness scale T is now varieii i will, knowing that any changes will be comp sated for by a corresponding corrective change in the value of R.

Inalikemannehifallomerlltdeeandecalee etandiethenpoeitlonedeothetthearm remainclampedandonlyoneelampilloosened. arrangedouthelndieiamembefllearriedthare'- W rolldlambylndlcateeonecalel'ontheihdiciamelnberfl themathematieal efleetofmaflhgaproportiontwenty pereent from the hlracterirtie reducatechmeineaehmemberoflluattonlothat tione muetbeuaed. Theeevarletlomm be the value ot the members. although changed determined by the speed operator. roiler. fore- Qnumerically. equaitoeaehother. mamorthepereondeelgnlngthelliderule.

remeine Itwlllbeunderetoodthattherearethreetypee Alithe other slidea Ilarethen eueeeellvely deaeflbed Alltheihdieatedmll turnlngtheclemningeerewll opening; for the reebecttverolletaum are M ll repreeentingthe standi'or reeordedandaenttotherollerahdallthemotor Theepeedofthemotot'fthelllt ltahd to: lethenaneertainedbymeaheofatachometerand ofetrlp. thebrideeismovedaotbattheaetuelmet 'l'headimtment ior'rollonening.wntspeedeefolmdislndicatedonthelealenofthe w ,ormotorepeedonanypartieidarstand elidelti'orthatstand. 'I'heotherllldeellanfl iamadebyturningtbeelatnllhgecrewflso thehboeitiohedeoaetoindieatetheactml' utorelwe thelllde 2| mtlng the roll torepeedeeeioundbytheaidofthetaehometer etandonwhichtheadiuetmentletobemadeand ontheotheretande,ahdtheconeetrollomiuthellideflismfledlndtheldlflltmentmlde arethennotedfromeaehoi'thethlckhrelative to the roll opening. oh aeale T. neroent eealee T. dl reductiononecaleormormeedonecalefi, Todeternunetheaetmpem 01mm. whicheverisdeeiredandtheelideiethen retionoocun'ingineaehetanmthemeearemcllmped and lked in Dodtln by mean; of the nipulated a; above and pereente'e of Mueclampingacrewll 'I'hlevillbefurtherdietionnotedontheslel? nmmedhereinafter. Tobalaneetmemlllw henmemtorgm 'I'headjuetmentfortbeflnllblnellleedlemde under exoeeeive loade. thealideruleleletto by movin: the brldse luembly which can-lee with aetuel rouing condition; at the time. The :lider it the motor speed acales R. The bridge i'l ie 2| are then adjuated to nermit lighter reductimg eo u eo look the bridge toeether with the slide: ie carried thereby m position. T mmm 'mam m' a Itwill be eeenthat the slidezruleofthepreeent of 'W pmmm'" mmm. m b' "med w a' I Q millfromagiveneineelahthellideruleisld invention has a number of useful functions. the

M mpomt W to ,mam the 00h upaethelheetwomdbemlled. Themotorlnead mezhecommuopemmmdmmm ticreductiomwlllbemadedneachoftheltan. ofeaehoftherolistandabymeaneofthisdenfimlndlodflhedn'ingmtherem viee,theeorreeeronmmnmtupn ehowntwoformeoi'auadditionaiaeelevhieh lcaleeDoi'theelidee|l.aehaebeendeecr-ibed. maybeinoorpontedwiththellldemleoreal. 7'. The slide 2| repreeentlng the laet flnigmng stand culator of the present invehtion If deeii'ed. The I. ie then poeitioned and clamped eo that the pointseale ae shown in l'lzure 9 combi-Ines ah lhdicla er 22 carried thereby indicatea the deeired thlckmember 21 can-ied by the bridge member I'l nese of the nniehed material oh thickneea scale T. which is eeeurely attached thereto hr any suitable 'Rae next to the last slide 2| repreaenting the roll manner ae at 2| and extende dovnvardly preferstandNmlOonthestandpredlngthelaet ablyfromtherlghthmdedgethereofmtbfl the sllde 2| representing roll stand No. Il or the.

last stand in the mill train parallel to the slides IB. However, this indicia member may be attached to the bridge in any other convenient position so long as it is parallel to the movement thereof. There is arranged on the indicia member 21, markings or a delivery speed scale F representing the speed of the strip in feet per minute as it is delivered from the last stand and the mill train. The upper pointer 24' arranged on the upper end of the slide 2| representing stand No. 11 is constructed so that it cooperates with both the speed scale R on slide IB and the delivery scale F on the indicia member 21. The delivery scale or markings F are arranged similar to the speed scale R, that is, inverted relative to the thickness scale T. The delivery scale F is also a logarithmic scale having the same base and same length per cycle as the other scales of the rule.

In Figure 10 there is shown another way in which the scale representing the speed of the strip as it is deliveredfrom the mill can be desig'ned. In this construction the delivery or marking scales F representing feet per minute are arranged on the upper end of the slide 2| representing roll stand No. 11 or the last stand just below the upper pointer 2| carried thereby and is inverted relative to the speed scales R. A pointer 29 which is adapted to cooperate with the scale F is securely attached to the right hand edge of bridge member |1 as at 30 and extends downwardly along the slide 2|. The pointer 29 is located relative to the scale by calculating the mili delivery speed for the same "setup" as is used in Originally calibrating the rule by the following equation:

(11) Delivery speed= and the pointer is arbitrarily mounted to indicate this value, at the same time making certain that all the values are set up according to Table III. It will be understood that the proper position of a logarithmic ruling for the delivery scales F is selected which covers the available range of the delivery speedof the mill. This range is obtained from the mill designer.

As a result of this invention it will be seen that there is provided a slide rule or calculator by which the mill loperator can easily and quickly determine the speed of the motor, the roll opening, and percent reduction of each of the roll stands and the speed of the strip as it is delivered from the mill for any desired thickness of flnished strip without any calculatlon or the aid of any other devices.

While I have in this application speclflcally described one embodlment and several modifications thereof which my invention may assume in practice, it will be understood that these embodiments are merely for the purpose of Illustration and description and that various other forms may be devised with-in the scope 'of my invention, as defined by the appended claims.

I claim:

1. A slide rule for the solution of a problem involving a number of unknown variables comprising a body member, a plurality of sets of slides arranged in parallel relation to each other on said body member, a bridge member arranged adjacent one end of said body member, said bridge member being arranged transversely of :"aid body .ranged on and adiacent the end of eac't scale on the next succeedi tioned slides and being position member and said sets of slides and 'beim longitudinally thereof, each of-said seW consisting of a pair of slides with one iongitudinally of the body member and being adjustably attached to said bridge 1 and extending alongside and between of said slides parallel thereto, scales ca. each of said slides representing the Varia tering into the general problem of the r all scales pertaining to each set of slides cc ing together an embociiment of one set o; between the variables of the rule :oral coacting to indicate on the various sc. values representing the unknown variab set in their proper relation to each other, of slides having at least one of the ciated therewith cooperating with 'the ceeding set of slides so that the slides can cessively positioned in the several set that the scales thereon will coact to in values of the unknown varables which wii all the relations severally embodied in ferent sets of slides of the rule.

2. A slide rule for the solution of a pro" volving a number of unknown variables w ing a body member, a plurality of slides in parallel relation in said body irnemll'eHC carried by said body member between eaM slides adjacent one end thereof, an inf slides cooperating with the scale located that slide and the next succeeding' slide, dicia member securely arranged on i slides intermediate the length thereof pe each other, each of said indicia meinii: a scale arranged along one edge 'there indicating means carried thereof which is adapted i movable bridge member are said body member and said. posite end thereof beyond tm plurality of spaced apart slide said bridge member, said s equal in number to the number o parallel thereto so as to provide a if of slides, each of said last menti bers having a scale arranged thereon movable relative to both said bridge said body member, an indieatm` scales of said second mentioned s they are adapted to cooperate, sai by the body member and each of the s" senting variables entering into the generw lem of the rule and all the scales i' any one set of slides oonstituting ioget bodiment of one set of relations het' varlables of the rule problem, and coa 't dicate on the various scales the value.C ing the unknown variables in that s'ei proper relation to each other with am, said slides adapted to be adjusted the known variables so as to indian known variables in that set and ti sets of slides adapted to be Suse relative thereto and coacting 'to values of the unknown variables w all the relations severally embodle ferent sets of slides of the rule.

3. In a device for determining the necessary in a mill train for produeir sheet of a predetermined thickness,

8 mimo tionoiabodymembenapluralityoisetsoislides arrangedinparalleirelationtoeachotherinsaid bodymemberandbeingequaiinnumbertothe numberoi'rollstandsinthemllltrain.abridge g memberarrangedadiacentoneendotsaidbody member. said bridge member being arranged transverselyotsaidbodymemberandsaidsetsoi slides and being movabie longitudinally thereoi. eachoisaidsetsotsiidesoiapairoi 10 slides with one arranged longitudinally oi the body member and the other being adiustably attached to said bridge member and extending alongsidetheother of saidsiides parallel thereto, scaiescarriedbysaldbodymemberandsaidsets il o! slides representing the variables including the roli opening. peresntage o! reduction. motor speed.anddiametsroftheroilswithallthescales pertainingtoeachsetoislidesconstitutingto- Iether the above named varlable iactors in one lrollstandandcoactingtoindicateonthevarious scaiesthevaluesrepresmtingtheunknownvariablesinthatstandintheirproperrelationto eachother,eachsetotslldeshavingatleastone of the scales associated therewith oooperating ll withthenextsucceedingsetotslidessothatthe' slides can be successively positioned in the several sets in order that the scales thereon will coact to indicate the values o! the above mentioned unknown variables on the scales of the other ot said asetsoislideswhichwillsatisi'yalltherelations severally embodied in the diil'erent sets ot slides and each roli stand.

4. In a device tor determining the adJustments neoessaryinamilltraini'orproducingaflnished u sheet oi a predetermined thickness. the combination o! a body member, a piurallty of sets ot slides arranged in parallel relation to each other on said bodymemberandbeingequalinnumberthe number o! roll stands in the mili train. a bridge w arranged adiacent one end of said body member. said bridge member being arranged transversely otsaidbodymemberandsaidsetsoi'slidesandbeing movable longitudinaiiy thereoi'. each of said setsoislides cousistingoiapairofslides withone 4' amneee longimalnuiy of the body member ana the other being adiustsbiy sttached to said bridge member and extending alongside and between the other o! said slides parallel thereto. each of said slides having thereon at least a logaiithmic scale u rcpresenting the diameter o! the rolls and another scale representing the speed of the motor with each scaie representing the diameter oi the rolls coacting with the oorresponding one o! a u pluraiity o! indicators associated with said bridge and each scaie representing the speed o! the motor coacting with a pointer carried by each o! the iongitudinaiiy extending slides. cooperable means arranged between said body member and each of .o the longitudinaily extending slides for indicatlng the ion opening. eaen of said longnudinauy eztending slides having a logarithmic scale secureiy arranged thereon representing the peroentage o! reduction. with said scales being substantially in parallel alignment with each other. each o! said last mentioned scales except the last one thereoi having a pointer i'or coacting with the graduations on the next su scaie.

5. In a device for determining the adjustments 7a necessary in a mili train ior producing a linished sheet of a predetermined thickness, the combination of a body member, a plurality of sets oi' slides arranged in parallel relation to each other in said body member and being equal in number to the 7| number of roll stands in the mili train, a bridge vot the scales associated therewith member arranged adiacent one end'oi said body member. said bridge member being arranged oi' said body member and said sets o! slides and being movabie longitudinally thereot. eachoisaidsetsoislidesconsistingoi'apalro! l slides with one arranged iongitudinally of the body member and the other being adiustabiy attached to said bridge member and e aiongside the other oi' said slide; parallel thereto.scaiescarried bysaidbodymemberandsaid 10 sets o! slides representing the variables inel the roli opening. percentage ot reduction. motor speed. and diameter oi' the rolls with all the scalm pertaining to each set o! slides constituting together the above named vari'able iactors in one 1| roli stand and coacting to indicate on the varioiu scales the values representing the unknown variabies in that -stand in their proper relation to each other. each set o i' slides having at least one cooperating with thenextsucceedingsetoi'siideasothatthe slides can be successively positioned in the severalsetsinorderthatthescalesthereonwillcoact to indicate the values of the above mentioned variables on the scales o! the other oi said sets oi' slides which will satisly all the relations severaliy embodied in the diii'erent sets od slides and each roli stand, and means carried by said bridge member cooperating with one o! said longitudinaliy extending slides tor indicating the a rateotspeedthesheetisbeingdeiiveredfrom the mili train.

6. In a device i'or determlnlng the adillstments necessary tor each unit ot a series o! interdependent mechanical operating units. the combination of a body member. a plurality o! sets o! slides arranged in parallel relation to each other and being naily thereoi. each of said sets o! slides consisting oi' a pair oi' slides with one arranged longitudinallyoi'thebodymemberand theotherbeingal adiustably attached to said bridge and extending along side oi' the other oi' said slides parallel thereto. scales carried by said body member and said sets of slides representing the variables of i eachoitheunitswithalithescalespertaining to each set o! slides constituting together an embodiment o! the variable iactors in one unit and coacting to indlcate on the various scales the values representing the unknown variabl in that unitintbeirproperreiationtoeachotherll sndwithanyonesetoisiidesadaptedtobeadtaining to that set oi slides, and the other oi' said sets of slides adapted to be successiveiy lo- 00 cated relative thereto and coacting to indicate the values o! the unknown variables on the other set oi' slides which will satisiy all the relations severally included in the diii'erent sets o! slides and each unit. aa

7. An apparatus ior determining the adiustment necessary tor each roll stand in a mill train i'or producing a flnished sheet o! predetermined thickness comprising a body member. a piurality of slides equal in number to the number 'lo o! roll stands in the mlll train secured to said body member at its lower end, logarithmic graduations on said body member between said slides tor iddicating the minimum and maximum rolling requirements i'or each roli stand in said mill 7| train, the last logarithmic graduation representing the last roll stand, pointers carried by said slides, the pointer on the last slide cooperating with the logarithmic graduations representing the last roll stand to indicate the metal thickness of the iinished product,logarithmic graduations carried by said slides and positioned above said first mentioned logarithmic graduations, pointers fixed to said slides for cooperation with said last mentioned logarithmic graduations to indicate the percentage reduction of the metal of the respective roll stands in thevmill train and a bridge adjustably attached to the body member transversely of said slides, slides carried by said bridge and extending between said first mentioned slides, upper and lower logarithmic graduations on said slides carried by said bridge, the

upper graduations'cooperating with a pointer car-.

ried by said bridge to determine the diameter of the rolls for each roll stand, the lower graduations cooperating with pointers carried by the first mentioned slides to indicate the speed of the motor for each roll stand.

8. In a calculator, the combination of a body, a plurality of sets of slides and a bridge, the bridge being adjustably attached to the body transversely of the said sets of slides, each set of slides comprising' a first slide and a second slide, the first slide being adiustably secured to the said bridge and having an upper set and a lower set of logarithmic graduations, each -upper set coacting with a corresponding one of a plurality of pointers fixed to the said bridge and each lower set of graduations coacting with an upper one of a set of two pointers fixed to each of the said second slides, each of the lower one of said two pointers coacting with a corresponding one of a series of parallel logarithmic scales stationarily attached to said body, each of said second' set of slides having a logarithmic scale fixedly secured thereon and forrning a series, each of the last named scales except the last one thereof having a pointer for coacting with the graduations of the next following of the said series.

9 A slide rule for the solution of a problem involving a number of unknown variables comprising a body member, a plurality of sets of slides arranged in parallel relation to each other on said body member, means arranged transversely of said body member and said sets of slides and which is movable longitudinally thereof. each of said sets of slides consisting of at least a pair of slides with one slide of each set attached to said movable transverse means and extending alongside and between the other of said slides parallel thereto which is carried by said body member, scales and indicators arranged on said slides with said scales representing the variables entering into the general problem of the rule with all scales pertaining to each set of slides constituting together an embodiment of one set of relations between the variables of the rule problem, and coacting to indicate on the various scales the values of the unknown variables in that set in their proper relation to each other, the other slide of each set of slides carried by the body member having a scale arranged thereon cooperating with an indicator on the corresponding slide of the next succeeding set. 'of slides so that the slides can be successively positioned in the several sets in order that the scales of each set will coact tov indicate the values of the unknown variables which will satisfy all the relations severally embodied in the different sets of slides of the rule.v

10. In a device for determining the adjustments necessary for each unit of a series of interdependent mechanical Operating units, the combination of a body member, a plurality of sets of slides arranged on said body member in parallel relation to each other and being equal in number to the number of mechanical units, a slidable member arranged transversely of said body member and said sets of slides and which ls movable longitudinally thereof, each of said sets of slides consisting of at least a pair of slides with one slide of each set attached to said slidable member and extending alongside and between the other of said slides which is carried by said body member, scales and indicators arranged on said slides with said scales representing the variables of each of the units with all the scales pertaining to each set of slides constituting together an embodiment of the variable factors in one unit and coacting to indicate on the various scales lthe valuesof the unknown variables in that unit in their proper relation to each other and with any one set of slides adapted to be adjusted according to the known variables so as to indicate the unknown variables in the unit pertaining to that set of slides. and the other of said sets of slides adapted to be successively located relative thereto and coacting to indicate 3.0 the values of the unknown variables on the other set of slides which will satisfy all the relations severally included in the different sets of slides and each unit.

11. In a device for determining the adJustments necessary for each unit of a series of interdependent mechanical Operating units, the combination of a body member, a plurality of sets of slides arranged on said body member in parallel relation to each other and being equal in 40 number to the number of mechanical units, a slidable member arranged transversely of said body member and said sets of slides and which is movable longitudinally thereof, each of said sets of slides consisting of at least a pair of slides with one slide of each set attached to said slidable member and extending alongside and between the other of said slides which is carried by said body member, scales and indicators arranged on said slides with said scales representing the variables of each of the units with all the scales pertaining to each set of slides constituting together an embodiment of the variable factors in one unit and coacting to indicate on the various scales the values of the unknown variables in that unit in their proper relation to each other, the other slide of each set of slides carried by the body member having a scale arranged thereon cooperating with an indicator on the corresponding slide of the next succeeding set 50 of slides in that the slides can be successively positioned in the several sets in order that the scales of each set will coact to indicate the values of the unknown variables which will satisfy all of the relations severauy embodied m the duferent sets of slides and each unit.

12. In a device for determining the adjustments necessary for each roll stand in a mili train for producing a flnished sheet of a prede-m termined thickness, the combination of a body member, a plurality of sets of slides arranged on said body member in parallel relation to each other. and being equal in number to the number of roll stands in the mili train, means arranged 7| transveraely of said body member and said sets of siides and which is movable lonsitudinally thereofreach of said sets of slides oonsistinz of atleastapairofslideswithonesiideofeach 5 set attached to said movable transverse means and extending alonzside and between the other ofsaidslidesparalleltheretowhichiscarried ny said body member. scales and indicators arranged on said slides with the scales representinz lo the variables including the roll opening, percentage of reductions, motor speed. and diameter oftherollswithallthescalespertaininztoeach set of slides constitutinz toeether the, above named variable factors in one roll stand and lcoactinstoindicateonthevarloussealesthe values of the unknown of the above variables inV that stand in their proper relation to each other,

the other slide of each set of slides carried by the body member having a scale arranzed thereon cooperating with an indicator on the correspondingslideotthenextsuooeedingsetofslides so that the slides can be successively positioned in the several sets in order that the scales of each set will coact to indicate the values of the above mentioned unknown variables on the sosie of the other of said sets of slides which will satisfy all the relations severally embodied in the diierent sets of slides and of each roll stand.

13. In a device for determininz the odinst- Mmentsnforeachrollstandinamill train for producing a flnished sheet of a predetermined thickness. the combination of a body member, a plurality of sets of slides arranzed on said body member in parallel relation to each ss otherandbeinzequalinnumbertothenumber centaa'e of reductions, motor speed. and diamete'r oftherollswithaiithescalespertaininztoeach set of slides constituting tocether the above named variable factora in one roll stand'and co- 15 actinztoindicateonthevariousscalesthevalues of the unknown of the above variahles in that standintheirproperreiationtoeachothenthe other slide of each set of siides carried by the that the slides can be succeasively positioned in the several sets in order that the scales of each set will coact to indicate the values of the above 25 mentioned imknown variables on the scale of the other of said sets of siides which will satisiy all the relations severally embodied in the different setsofslidesandofeachrollstand.andmeans carried by said transversely arranzed means co- Operating with any one of said slides carried by thebodymemberforindicatinztherateofspeed the sheet is being delivered from the milLtrain.

HOWARD C. GOODRICH. 86 

